Gibbs constant

The universal overshoot fraction, about 8.95% of the jump size, in the Gibbs phenomenon.

The Gibbs constant is the fixed fraction of a jump's size, approximately $8.95\%$ , that a Fourier partial sum's overshoot converges to near that jump. It is the same for any piecewise-smooth function's jump, not just one particular waveform, because the local behavior of a partial sum near a jump depends only on the jump's size, not on the rest of the function.

Examples

A jump of height 2 produces an overshoot of about $2\times0.0895\approx0.179$ , regardless of the function's shape elsewhere.